Problem: Simplify the expression. $(-4q^{3}+6q)(3q^{3}+3q^{2}+6q)$
Explanation: First use the distributive property. $ - 4 q^3 (3 q^3) - 4 q^3 (3 q^2) - 4 q^3 (6 q) + 6 q (3 q^3) + 6 q (3 q^2) + 6 q (6 q) $ Simplify. $ - 12q^{6} - 12q^{5} - 24q^{4} + 18q^{4} + 18q^{3} + 36q^{2} $ $-12q^{6}-12q^{5}-6q^{4}+18q^{3}+36q^{2}$ Identify like terms. $ {- 12q^{6}} {- 12q^{5}} {- 24q^{4}} {+ 18q^{4}} {+ 18q^{3}} {+ 36q^{2}} $ Add the coefficients. $ { -12q^{6}} { -12q^{5}} { -6q^{4}} {+ 18q^{3}} {+ 36q^{2}} $